Canadian Computing Competition: 2022 Stage 1, Senior #4
Andrew is a very curious student who drew a circle with the center at and an integer circumference of . The location of a point on the circle is the counter-clockwise arc length from the right-most point of the circle.
Andrew drew points at integer locations. In particular, the point is drawn at location . It is possible for Andrew to draw multiple points at the same location.
A good triplet is defined as a triplet that satisfies the following conditions:
- The origin lies strictly inside the triangle with vertices at , , and . In particular, the origin is not on the triangle's perimeter.
Lastly, two triplets and are distinct if , , or .
Andrew, being a curious student, wants to know the number of distinct good triplets. Please help him determine this number.
The first line contains the integers and , separated by one space.
The second line contains space-separated integers. The integer is .
The following table shows how the available 15 marks are distributed.
|Marks Awarded||Number of Points||Circumference||Additional Constraints|
|marks||are all distinct (i.e., every location contains at most one point)|
Output the number of distinct good triplets.
8 10 0 2 5 5 6 9 0 0
Output for Sample Input
Explanation of Output for Sample Input
Andrew drew the following diagram.
The origin lies strictly inside the triangle with vertices , , and , so is a good triplet. The other five good triplets are , , , , and .